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If 6/(x(x+1))>1, which of the following could the value of x?
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21 Dec 2014, 16:23
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If \(\frac{6}{x(x+1)}>1\), which of the following could the value of x? A. 3.5 B. 2.5 C. 2.5 D. 3.5 E. 4.5
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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21 Dec 2014, 19:11
Hi viktorija, This question can be solved by TESTing THE ANSWERS. One (and only one) or those numbers could be a solution to the given inequality, so we could check them (just plug them in) until we find one that "fits" the given inequality. There is a logical math shortcut here though that we can take advantage of: We're told that 6/(product) > 1 so the denominator must be LESS than 6. That way 6/(less than 6) will be > 1. So we're really just looking for a product that's less than 6. Logically, we're probably looking for a value for X that's relatively close to 0, so let's check answers B and C....But don't do the math just yet... Answer B: X = 2.5 Denominator = (2.5)(1.5) Answer C: X = 2.5 Denominator = (2.5)(3.5) Since the negative signs will cancel out in Answer B, you don't have to do the math to see that Answer B is smaller. Since there's only one answer that will "fit", it has to be B. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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10 Jan 2015, 02:19
If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ?
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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10 Jan 2015, 04:26
Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check!



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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10 Jan 2015, 06:01
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 \(\frac{6}{x(x+1)} >1\) let's analyze the denominator. x(x+1) = x^2+x. now x^2+x will always be positive except for numbers lying between 1 and 0. now if x lies between 1 and 0, then the fraction \(\frac{6}{x(x+1)}\) will be negative. this violates our initial given condition that \(\frac{6}{x(x+1)} >1\). hence the expression x^2+x will always be positive. now since expression x^2+x is positive, therefore we can cross multiply. Thus we have x^2+x<6 x^2+x6<0 (x+3)(x2)<0 now for all values of x which are less than 3, (x+3)(x2) will always be positive. similarly for all values of x , which are greater than 2, (x+3)(x2) will always be positive. hence our desired range is between 3 and 2. i.e. 3<x<2. now out of the given options, only option b lies inside this range. hence answer must be B



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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10 Jan 2015, 06:46
sytabish wrote: Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check! thanks . actually we do not need know the sign of X here Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1)) 6 > (x(x+1)) 6> x^2 + x x^2+x6 < 0 (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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10 Jan 2015, 13:37
Hi styabish, You have to be very careful with your assumptions in the Quant section. This specific Number Property WILL show up on Test Day.... (X)(X+1) = positive This does NOT mean that X has to be positive. X COULD be positive.... eg X = 1 (1)(2) = 2 X COULD be NEGATIVE though... eg X = 2 (2)(1) = 2 GMAT assassins aren't born, they're made, Rich
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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12 Jan 2015, 21:56
\(\frac{6}{(x(x+1))} > 1\) \(\frac{6}{x^2 + x} > 1\) For x = 3.5 \(\frac{6}{12.253.5}\) >> This would be less than 1 For x = 2.5 \(\frac{6}{6.252.5}\) >> This would be greater than 1 Answer = B
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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21 Aug 2015, 08:27
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2 then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please?



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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21 Aug 2015, 08:36



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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21 Aug 2015, 08:41
aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement. Additionally, for algebraic solution, look below: Given : \(\frac{6}{x(x+1)} > 1\) > \(\frac{6}{x(x+1)}  1 > 0\) > \(\frac{6x^2x}{x(x+1)} > 0\) > \(\frac{6+x^2+x}{x(x+1)} < 0\) \(\frac{(x+3)(x2)}{x(x+1)} < 0\) > 3<x<1 or 0<x<2 Only 2.5 lies in this range. Hope this helps.



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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Updated on: 27 Aug 2015, 02:19
Bunuel wrote: aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2 then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? Let me ask you: what does x < 3 (x is less than 3) or x < 2 (x is less than 2) even mean? As for the solution please see above. This link sorted my worries! For anyone who struggled in the last bit after factorising refer this: https://www.khanacademy.org/math/algebr ... equalitiesThanks Bunuel! Now I know why did you ask me what didx < 3 (x is less than 3) or x < 2 (x is less than 2) even mean?
Originally posted by aggarwalpooja on 21 Aug 2015, 08:58.
Last edited by aggarwalpooja on 27 Aug 2015, 02:19, edited 1 time in total.



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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21 Aug 2015, 09:15
Engr2012 wrote: aggarwalpooja wrote: viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 isn't this what you get after factorising x<3 or x<2then how is 2.5 the answer? (since 2.5 is greater than 3) Can someone help, please? The most straightforward method for this type of question will be to use the values in the options and see which one gives you >1 . Only 1 option must satisfy this requirement. Additionally, for algebraic solution, look below: Given : \(\frac{6}{x(x+1)} > 1\) > \(\frac{6}{x(x+1)}  1 > 0\) > \(\frac{6x^2x}{x(x+1)} > 0\) > \(\frac{6+x^2+x}{x(x+1)} < 0\) \(\frac{(x+3)(x2)}{x(x+1)} < 0\) > 3<x<1 or 0<x<2 Only 2.5 lies in this range. Hope this helps. Thanks Engr12, plugging in the value is guess the easiest!



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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02 Jan 2017, 13:43
\(\frac{6}{(x(x+1))} > 1\) 6 > x(x+1) \(6 > x^{2} + x\) Plug In options B
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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20 Feb 2018, 11:10
Lucky2783 wrote: sytabish wrote: Lucky2783 wrote: If 6/(x(x+1))>1, which of the following could the value of x? A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 Given 6/(x(x+1))>1 i.e x(x+1) is +ive implies X is positive ; since we are dealing with all positives 6/(x(x+1))>1 > (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 Bunuel am i doing right ? Lucky2783 ,I don't think this derivation of yours is right: x(x+1) is +ive implies X is positive. Please check! thanks . actually we do not need know the sign of X here Given 6/(x(x+1))>1 implies (x(x+1)) is a +ive quantity so we can simply multilply both sides of inequality by (x(x+1)) 6 > (x(x+1)) 6> x^2 + x x^2+x6 < 0 (x+3)(x2)<0 ++++++(3)(2)++++++ so anything between 3 and 2 satisfies the inequality . B. 2.5 hello there! How did you manage to draw the line based on this (x+3)(x2)<0 is there rule to transform it into line ? thank you
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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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13 Sep 2018, 16:24
Hi dave13, Let me try to respond to your query. If \(\frac{6}{x(x+1)}\)>1, which of the following could the value of x? note x and (x+1) are two consecutive numbers, then their product is always positive . Why if x is negative then (x+1) is also negative and their product is always positive if x is positive then (x+1) is also positive and their product is always positive But x cannot be 1 and 0 , because the exp will be undefined for these values. So we can write \(\frac{6}{x(x+1)}\)>1 as \(\frac{6}{x(x+1)}\)1>0 So \(\frac{(6x(x+1)}{x(x+1)}\)>0 \(\frac{(6x^2x)}{x(x+1)}\)>0 \(\frac{((x+3)(x2))}{x(x+1)}\)>0 When we multiply by 1 on both sides we change the sign of inequality. \(\frac{((x+3)(x2))}{x(x+1)}\)<0 Now if you draw the number line and have positive and negative regions this is how it would look ++++++++++++(3)(1)++++++++++++(0)(2)++++++++++ Now the region where the inequality holds is 3<x<1 and 0<x<2 Now options B, C, D are greater than 2 so discard. Option A is less than 3 so discard Option B lies between 3<x<1 so this could be possible value of for which the inequality will hold. Probus



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Re: If 6/(x(x+1))>1, which of the following could the value of x?
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14 Sep 2018, 06:09
viktorija wrote: If 6/(x(x+1))>1, which of the following could the value of x?
A.3.5 B.2.5 C.2.5 D.3.5 E.4.5 \(\frac{6}{[x (x + 1)]}\)\(> 1\) \(\frac{6}{[x^2 + x]}\) > 1 We know that \(x^2 + x\) can never be negative irrespective of the value of \("x"\), therefore \(6 > x^2 + x\) Or \(x^2 + x  6 < 0\) \((x + 3) (x  2) < 0\) \((x  2) < 0\) or \((x + 3) > 0\) \(x < 2\) or \(x > 3\) \(3 < x < 2\) Answer : B = \(2.5\)
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